text: 
  # pylint: disable=E1101,E1103,W0232
  import datetime
  from sys import getsizeof
  import warnings
  
  import numpy as np
  
  from pandas._libs import (
      Timestamp, algos as libalgos, index as libindex, lib, tslibs)
  import pandas.compat as compat
  from pandas.compat import lrange, lzip, map, range, zip
  from pandas.compat.numpy import function as nv
  from pandas.errors import PerformanceWarning, UnsortedIndexError
  from pandas.util._decorators import Appender, cache_readonly
  
  from pandas.core.dtypes.common import (
      ensure_int64, ensure_platform_int, is_categorical_dtype, is_hashable,
      is_integer, is_iterator, is_list_like, is_object_dtype, is_scalar,
      pandas_dtype)
  from pandas.core.dtypes.dtypes import ExtensionDtype, PandasExtensionDtype
  from pandas.core.dtypes.missing import array_equivalent, isna
  
  import pandas.core.algorithms as algos
  import pandas.core.common as com
  from pandas.core.config import get_option
  import pandas.core.indexes.base as ibase
  from pandas.core.indexes.base import (
      Index, InvalidIndexError, _index_shared_docs, ensure_index)
  from pandas.core.indexes.frozen import FrozenList, _ensure_frozen
  import pandas.core.missing as missing
  
  from pandas.io.formats.printing import pprint_thing
  
  _index_doc_kwargs = dict(ibase._index_doc_kwargs)
  _index_doc_kwargs.update(
      dict(klass='MultiIndex',
           target_klass='MultiIndex or list of tuples'))
  
  
  class MultiIndexUIntEngine(libindex.BaseMultiIndexCodesEngine,
                             libindex.UInt64Engine):
      """
      This class manages a MultiIndex by mapping label combinations to positive
      integers.
      """
      _base = libindex.UInt64Engine
  
      def _codes_to_ints(self, codes):
          """
          Transform combination(s) of uint64 in one uint64 (each), in a strictly
          monotonic way (i.e. respecting the lexicographic order of integer
          combinations): see BaseMultiIndexCodesEngine documentation.
  
          Parameters
          ----------
          codes : 1- or 2-dimensional array of dtype uint64
              Combinations of integers (one per row)
  
          Returns
          ------
          int_keys : scalar or 1-dimensional array, of dtype uint64
              Integer(s) representing one combination (each)
          """
          # Shift the representation of each level by the pre-calculated number
          # of bits:
          codes <<= self.offsets
  
          # Now sum and OR are in fact interchangeable. This is a simple
          # composition of the (disjunct) significant bits of each level (i.e.
          # each column in "codes") in a single positive integer:
          if codes.ndim == 1:
              # Single key
              return np.bitwise_or.reduce(codes)
  
          # Multiple keys
          return np.bitwise_or.reduce(codes, axis=1)
  
  
  class MultiIndexPyIntEngine(libindex.BaseMultiIndexCodesEngine,
                              libindex.ObjectEngine):
      """
      This class manages those (extreme) cases in which the number of possible
      label combinations overflows the 64 bits integers, and uses an ObjectEngine
      containing Python integers.
      """
      _base = libindex.ObjectEngine
  
      def _codes_to_ints(self, codes):
          """
          Transform combination(s) of uint64 in one Python integer (each), in a
          strictly monotonic way (i.e. respecting the lexicographic order of
          integer combinations): see BaseMultiIndexCodesEngine documentation.
  
          Parameters
          ----------
          codes : 1- or 2-dimensional array of dtype uint64
              Combinations of integers (one per row)
  
          Returns
          ------
          int_keys : int, or 1-dimensional array of dtype object
              Integer(s) representing one combination (each)
          """
  
          # Shift the representation of each level by the pre-calculated number
          # of bits. Since this can overflow uint64, first make sure we are
          # working with Python integers:
          codes = codes.astype('object') << self.offsets
  
          # Now sum and OR are in fact interchangeable. This is a simple
          # composition of the (disjunct) significant bits of each level (i.e.
          # each column in "codes") in a single positive integer (per row):
          if codes.ndim == 1:
              # Single key
              return np.bitwise_or.reduce(codes)
  
          # Multiple keys
          return np.bitwise_or.reduce(codes, axis=1)
  
  
  class MultiIndex(Index):
      """
      A multi-level, or hierarchical, index object for pandas objects.
  
      Parameters
      ----------
      levels : sequence of arrays
          The unique labels for each level
      labels : sequence of arrays
          Integers for each level designating which label at each location
      sortorder : optional int
          Level of sortedness (must be lexicographically sorted by that
          level)
      names : optional sequence of objects
          Names for each of the index levels. (name is accepted for compat)
      copy : boolean, default False
          Copy the meta-data
      verify_integrity : boolean, default True
          Check that the levels/labels are consistent and valid
  
      Examples
      ---------
      A new ``MultiIndex`` is typically constructed using one of the helper
      methods :meth:`MultiIndex.from_arrays`, :meth:`MultiIndex.from_product`
      and :meth:`MultiIndex.from_tuples`. For example (using ``.from_arrays``):
  
      >>> arrays = [[1, 1, 2, 2], ['red', 'blue', 'red', 'blue']]
      >>> pd.MultiIndex.from_arrays(arrays, names=('number', 'color'))
      MultiIndex(levels=[[1, 2], ['blue', 'red']],
             labels=[[0, 0, 1, 1], [1, 0, 1, 0]],
             names=['number', 'color'])
  
      See further examples for how to construct a MultiIndex in the doc strings
      of the mentioned helper methods.
  
      Notes
      -----
      See the `user guide
      <http://pandas.pydata.org/pandas-docs/stable/advanced.html>`_ for more.
  
      See Also
      --------
      MultiIndex.from_arrays  : Convert list of arrays to MultiIndex.
      MultiIndex.from_product : Create a MultiIndex from the cartesian product
                                of iterables.
      MultiIndex.from_tuples  : Convert list of tuples to a MultiIndex.
      Index : The base pandas Index type.
  
      Attributes
      ----------
      names
      levels
      labels
      nlevels
      levshape
  
      Methods
      -------
      from_arrays
      from_tuples
      from_product
      set_levels
      set_labels
      to_frame
      to_flat_index
      is_lexsorted
      sortlevel
      droplevel
      swaplevel
      reorder_levels
      remove_unused_levels
      """
  
      # initialize to zero-length tuples to make everything work
      _typ = 'multiindex'
      _names = FrozenList()
      _levels = FrozenList()
      _labels = FrozenList()
      _comparables = ['names']
      rename = Index.set_names
  
      # --------------------------------------------------------------------
      # Constructors
  
      def __new__(cls, levels=None, labels=None, sortorder=None, names=None,
                  dtype=None, copy=False, name=None,
                  verify_integrity=True, _set_identity=True):
  
          # compat with Index
          if name is not None:
              names = name
          if levels is None or labels is None:
              raise TypeError("Must pass both levels and labels")
          if len(levels) != len(labels):
              raise ValueError('Length of levels and labels must be the same.')
          if len(levels) == 0:
              raise ValueError('Must pass non-zero number of levels/labels')
  
          result = object.__new__(MultiIndex)
  
          # we've already validated levels and labels, so shortcut here
          result._set_levels(levels, copy=copy, validate=False)
          result._set_labels(labels, copy=copy, validate=False)
  
          if names is not None:
              # handles name validation
              result._set_names(names)
  
          if sortorder is not None:
              result.sortorder = int(sortorder)
          else:
              result.sortorder = sortorder
  
          if verify_integrity:
              result._verify_integrity()
          if _set_identity:
              result._reset_identity()
          return result
  
      def _verify_integrity(self, labels=None, levels=None):
          """
  
          Parameters
          ----------
          labels : optional list
              Labels to check for validity. Defaults to current labels.
          levels : optional list
              Levels to check for validity. Defaults to current levels.
  
          Raises
          ------
          ValueError
              If length of levels and labels don't match, if any label would
              exceed level bounds, or there are any duplicate levels.
          """
          # NOTE: Currently does not check, among other things, that cached
          # nlevels matches nor that sortorder matches actually sortorder.
          labels = labels or self.labels
          levels = levels or self.levels
  
          if len(levels) != len(labels):
              raise ValueError("Length of levels and labels must match. NOTE:"
                               " this index is in an inconsistent state.")
          label_length = len(self.labels[0])
          for i, (level, label) in enumerate(zip(levels, labels)):
              if len(label) != label_length:
                  raise ValueError("Unequal label lengths: %s" %
                                   ([len(lab) for lab in labels]))
              if len(label) and label.max() >= len(level):
                  raise ValueError("On level %d, label max (%d) >= length of"
                                   " level  (%d). NOTE: this index is in an"
                                   " inconsistent state" % (i, label.max(),
                                                            len(level)))
              if not level.is_unique:
                  raise ValueError("Level values must be unique: {values} on "
                                   "level {level}".format(
                                       values=[value for value in level],
                                       level=i))
  
      @classmethod
      def from_arrays(cls, arrays, sortorder=None, names=None):
          """
          Convert arrays to MultiIndex
  
          Parameters
          ----------
          arrays : list / sequence of array-likes
              Each array-like gives one level's value for each data point.
              len(arrays) is the number of levels.
          sortorder : int or None
              Level of sortedness (must be lexicographically sorted by that
              level)
  
          Returns
          -------
          index : MultiIndex
  
          Examples
          --------
          >>> arrays = [[1, 1, 2, 2], ['red', 'blue', 'red', 'blue']]
          >>> pd.MultiIndex.from_arrays(arrays, names=('number', 'color'))
  
          See Also
          --------
          MultiIndex.from_tuples : Convert list of tuples to MultiIndex.
          MultiIndex.from_product : Make a MultiIndex from cartesian product
                                    of iterables.
          """
          if not is_list_like(arrays):
              raise TypeError("Input must be a list / sequence of array-likes.")
          elif is_iterator(arrays):
              arrays = list(arrays)
  
          # Check if lengths of all arrays are equal or not,
          # raise ValueError, if not
          for i in range(1, len(arrays)):
              if len(arrays[i]) != len(arrays[i - 1]):
                  raise ValueError('all arrays must be same length')
  
          from pandas.core.arrays.categorical import _factorize_from_iterables
  
          labels, levels = _factorize_from_iterables(arrays)
          if names is None:
              names = [getattr(arr, "name", None) for arr in arrays]
  
          return MultiIndex(levels=levels, labels=labels, sortorder=sortorder,
                            names=names, verify_integrity=False)
  
      @classmethod
      def from_tuples(cls, tuples, sortorder=None, names=None):
          """
          Convert list of tuples to MultiIndex
  
          Parameters
          ----------
          tuples : list / sequence of tuple-likes
              Each tuple is the index of one row/column.
          sortorder : int or None
              Level of sortedness (must be lexicographically sorted by that
              level)
  
          Returns
          -------
          index : MultiIndex
  
          Examples
          --------
          >>> tuples = [(1, u'red'), (1, u'blue'),
                        (2, u'red'), (2, u'blue')]
          >>> pd.MultiIndex.from_tuples(tuples, names=('number', 'color'))
  
          See Also
          --------
          MultiIndex.from_arrays : Convert list of arrays to MultiIndex
          MultiIndex.from_product : Make a MultiIndex from cartesian product
                                    of iterables
          """
          if not is_list_like(tuples):
              raise TypeError('Input must be a list / sequence of tuple-likes.')
          elif is_iterator(tuples):
              tuples = list(tuples)
  
          if len(tuples) == 0:
              if names is None:
                  msg = 'Cannot infer number of levels from empty list'
                  raise TypeError(msg)
              arrays = [[]] * len(names)
          elif isinstance(tuples, (np.ndarray, Index)):
              if isinstance(tuples, Index):
                  tuples = tuples._values
  
              arrays = list(lib.tuples_to_object_array(tuples).T)
          elif isinstance(tuples, list):
              arrays = list(lib.to_object_array_tuples(tuples).T)
          else:
              arrays = lzip(*tuples)
  
          return MultiIndex.from_arrays(arrays, sortorder=sortorder, names=names)
  
      @classmethod
      def from_product(cls, iterables, sortorder=None, names=None):
          """
          Make a MultiIndex from the cartesian product of multiple iterables
  
          Parameters
          ----------
          iterables : list / sequence of iterables
              Each iterable has unique labels for each level of the index.
          sortorder : int or None
              Level of sortedness (must be lexicographically sorted by that
              level).
          names : list / sequence of strings or None
              Names for the levels in the index.
  
          Returns
          -------
          index : MultiIndex
  
          Examples
          --------
          >>> numbers = [0, 1, 2]
          >>> colors = [u'green', u'purple']
          >>> pd.MultiIndex.from_product([numbers, colors],
                                         names=['number', 'color'])
          MultiIndex(levels=[[0, 1, 2], [u'green', u'purple']],
                     labels=[[0, 0, 1, 1, 2, 2], [0, 1, 0, 1, 0, 1]],
                     names=[u'number', u'color'])
  
          See Also
          --------
          MultiIndex.from_arrays : Convert list of arrays to MultiIndex.
          MultiIndex.from_tuples : Convert list of tuples to MultiIndex.
          """
          from pandas.core.arrays.categorical import _factorize_from_iterables
          from pandas.core.reshape.util import cartesian_product
  
          if not is_list_like(iterables):
              raise TypeError("Input must be a list / sequence of iterables.")
          elif is_iterator(iterables):
              iterables = list(iterables)
  
          labels, levels = _factorize_from_iterables(iterables)
          labels = cartesian_product(labels)
          return MultiIndex(levels, labels, sortorder=sortorder, names=names)
  
      # --------------------------------------------------------------------
  
      @property
      def levels(self):
          return self._levels
  
      @property
      def _values(self):
          # We override here, since our parent uses _data, which we dont' use.
          return self.values
  
      @property
      def array(self):
          """
          Raises a ValueError for `MultiIndex` because there's no single
          array backing a MultiIndex.
  
          Raises
          ------
          ValueError
          """
          msg = ("MultiIndex has no single backing array. Use "
                 "'MultiIndex.to_numpy()' to get a NumPy array of tuples.")
          raise ValueError(msg)
  
      @property
      def _is_homogeneous_type(self):
          """Whether the levels of a MultiIndex all have the same dtype.
  
          This looks at the dtypes of the levels.
  
          See Also
          --------
          Index._is_homogeneous_type
          DataFrame._is_homogeneous_type
  
          Examples
          --------
          >>> MultiIndex.from_tuples([
          ...     ('a', 'b'), ('a', 'c')])._is_homogeneous_type
          True
          >>> MultiIndex.from_tuples([
          ...     ('a', 1), ('a', 2)])._is_homogeneous_type
          False
          """
          return len({x.dtype for x in self.levels}) <= 1
  
      def _set_levels(self, levels, level=None, copy=False, validate=True,
                      verify_integrity=False):
          # This is NOT part of the levels property because it should be
          # externally not allowed to set levels. User beware if you change
          # _levels directly
          if validate and len(levels) == 0:
              raise ValueError('Must set non-zero number of levels.')
          if validate and level is None and len(levels) != self.nlevels:
              raise ValueError('Length of levels must match number of levels.')
          if validate and level is not None and len(levels) != len(level):
              raise ValueError('Length of levels must match length of level.')
  
          if level is None:
              new_levels = FrozenList(
                  ensure_index(lev, copy=copy)._shallow_copy()
                  for lev in levels)
          else:
              level = [self._get_level_number(l) for l in level]
              new_levels = list(self._levels)
              for l, v in zip(level, levels):
                  new_levels[l] = ensure_index(v, copy=copy)._shallow_copy()
              new_levels = FrozenList(new_levels)
  
          if verify_integrity:
              self._verify_integrity(levels=new_levels)
  
          names = self.names
          self._levels = new_levels
          if any(names):
              self._set_names(names)
  
          self._tuples = None
          self._reset_cache()
  
      def set_levels(self, levels, level=None, inplace=False,
                     verify_integrity=True):
          """
          Set new levels on MultiIndex. Defaults to returning
          new index.
  
          Parameters
          ----------
          levels : sequence or list of sequence
              new level(s) to apply
          level : int, level name, or sequence of int/level names (default None)
              level(s) to set (None for all levels)
          inplace : bool
              if True, mutates in place
          verify_integrity : bool (default True)
              if True, checks that levels and labels are compatible
  
          Returns
          -------
          new index (of same type and class...etc)
  
          Examples
          --------
          >>> idx = pd.MultiIndex.from_tuples([(1, u'one'), (1, u'two'),
                                              (2, u'one'), (2, u'two')],
                                              names=['foo', 'bar'])
          >>> idx.set_levels([['a','b'], [1,2]])
          MultiIndex(levels=[[u'a', u'b'], [1, 2]],
                     labels=[[0, 0, 1, 1], [0, 1, 0, 1]],
                     names=[u'foo', u'bar'])
          >>> idx.set_levels(['a','b'], level=0)
          MultiIndex(levels=[[u'a', u'b'], [u'one', u'two']],
                     labels=[[0, 0, 1, 1], [0, 1, 0, 1]],
                     names=[u'foo', u'bar'])
          >>> idx.set_levels(['a','b'], level='bar')
          MultiIndex(levels=[[1, 2], [u'a', u'b']],
                     labels=[[0, 0, 1, 1], [0, 1, 0, 1]],
                     names=[u'foo', u'bar'])
          >>> idx.set_levels([['a','b'], [1,2]], level=[0,1])
          MultiIndex(levels=[[u'a', u'b'], [1, 2]],
                     labels=[[0, 0, 1, 1], [0, 1, 0, 1]],
                     names=[u'foo', u'bar'])
          """
          if is_list_like(levels) and not isinstance(levels, Index):
              levels = list(levels)
  
          if level is not None and not is_list_like(level):
              if not is_list_like(levels):
                  raise TypeError("Levels must be list-like")
              if is_list_like(levels[0]):
                  raise TypeError("Levels must be list-like")
              level = [level]
              levels = [levels]
          elif level is None or is_list_like(level):
              if not is_list_like(levels) or not is_list_like(levels[0]):
                  raise TypeError("Levels must be list of lists-like")
  
          if inplace:
              idx = self
          else:
              idx = self._shallow_copy()
          idx._reset_identity()
          idx._set_levels(levels, level=level, validate=True,
                          verify_integrity=verify_integrity)
          if not inplace:
              return idx
  
      @property
      def labels(self):
          return self._labels
  
      def _set_labels(self, labels, level=None, copy=False, validate=True,
                      verify_integrity=False):
  
          if validate and level is None and len(labels) != self.nlevels:
              raise ValueError("Length of labels must match number of levels")
          if validate and level is not None and len(labels) != len(level):
              raise ValueError('Length of labels must match length of levels.')
  
          if level is None:
              new_labels = FrozenList(
                  _ensure_frozen(lab, lev, copy=copy)._shallow_copy()
                  for lev, lab in zip(self.levels, labels))
          else:
              level = [self._get_level_number(l) for l in level]
              new_labels = list(self._labels)
              for lev_idx, lab in zip(level, labels):
                  lev = self.levels[lev_idx]
                  new_labels[lev_idx] = _ensure_frozen(
                      lab, lev, copy=copy)._shallow_copy()
              new_labels = FrozenList(new_labels)
  
          if verify_integrity:
              self._verify_integrity(labels=new_labels)
  
          self._labels = new_labels
          self._tuples = None
          self._reset_cache()
  
      def set_labels(self, labels, level=None, inplace=False,
                     verify_integrity=True):
          """
          Set new labels on MultiIndex. Defaults to returning
          new index.
  
          Parameters
          ----------
          labels : sequence or list of sequence
              new labels to apply
          level : int, level name, or sequence of int/level names (default None)
              level(s) to set (None for all levels)
          inplace : bool
              if True, mutates in place
          verify_integrity : bool (default True)
              if True, checks that levels and labels are compatible
  
          Returns
          -------
          new index (of same type and class...etc)
  
          Examples
          --------
          >>> idx = pd.MultiIndex.from_tuples([(1, u'one'), (1, u'two'),
                                              (2, u'one'), (2, u'two')],
                                              names=['foo', 'bar'])
          >>> idx.set_labels([[1,0,1,0], [0,0,1,1]])
          MultiIndex(levels=[[1, 2], [u'one', u'two']],
                     labels=[[1, 0, 1, 0], [0, 0, 1, 1]],
                     names=[u'foo', u'bar'])
          >>> idx.set_labels([1,0,1,0], level=0)
          MultiIndex(levels=[[1, 2], [u'one', u'two']],
                     labels=[[1, 0, 1, 0], [0, 1, 0, 1]],
                     names=[u'foo', u'bar'])
          >>> idx.set_labels([0,0,1,1], level='bar')
          MultiIndex(levels=[[1, 2], [u'one', u'two']],
                     labels=[[0, 0, 1, 1], [0, 0, 1, 1]],
                     names=[u'foo', u'bar'])
          >>> idx.set_labels([[1,0,1,0], [0,0,1,1]], level=[0,1])
          MultiIndex(levels=[[1, 2], [u'one', u'two']],
                     labels=[[1, 0, 1, 0], [0, 0, 1, 1]],
                     names=[u'foo', u'bar'])
          """
          if level is not None and not is_list_like(level):
              if not is_list_like(labels):
                  raise TypeError("Labels must be list-like")
              if is_list_like(labels[0]):
                  raise TypeError("Labels must be list-like")
              level = [level]
              labels = [labels]
          elif level is None or is_list_like(level):
              if not is_list_like(labels) or not is_list_like(labels[0]):
                  raise TypeError("Labels must be list of lists-like")
  
          if inplace:
              idx = self
          else:
              idx = self._shallow_copy()
          idx._reset_identity()
          idx._set_labels(labels, level=level, verify_integrity=verify_integrity)
          if not inplace:
              return idx
  
      def copy(self, names=None, dtype=None, levels=None, labels=None,
               deep=False, _set_identity=False, **kwargs):
          """
          Make a copy of this object. Names, dtype, levels and labels can be
          passed and will be set on new copy.
  
          Parameters
          ----------
          names : sequence, optional
          dtype : numpy dtype or pandas type, optional
          levels : sequence, optional
          labels : sequence, optional
  
          Returns
          -------
          copy : MultiIndex
  
          Notes
          -----
          In most cases, there should be no functional difference from using
          ``deep``, but if ``deep`` is passed it will attempt to deepcopy.
          This could be potentially expensive on large MultiIndex objects.
          """
          name = kwargs.get('name')
          names = self._validate_names(name=name, names=names, deep=deep)
  
          if deep:
              from copy import deepcopy
              if levels is None:
                  levels = deepcopy(self.levels)
              if labels is None:
                  labels = deepcopy(self.labels)
          else:
              if levels is None:
                  levels = self.levels
              if labels is None:
                  labels = self.labels
          return MultiIndex(levels=levels, labels=labels, names=names,
                            sortorder=self.sortorder, verify_integrity=False,
                            _set_identity=_set_identity)
  
      def __array__(self, dtype=None):
          """ the array interface, return my values """
          return self.values
  
      def view(self, cls=None):
          """ this is defined as a copy with the same identity """
          result = self.copy()
          result._id = self._id
          return result
  
      def _shallow_copy_with_infer(self, values, **kwargs):
          # On equal MultiIndexes the difference is empty.
          # Therefore, an empty MultiIndex is returned GH13490
          if len(values) == 0:
              return MultiIndex(levels=[[] for _ in range(self.nlevels)],
                                labels=[[] for _ in range(self.nlevels)],
                                **kwargs)
          return self._shallow_copy(values, **kwargs)
  
      @Appender(_index_shared_docs['__contains__'] % _index_doc_kwargs)
      def __contains__(self, key):
          hash(key)
          try:
              self.get_loc(key)
              return True
          except (LookupError, TypeError):
              return False
  
      contains = __contains__
  
      @Appender(_index_shared_docs['_shallow_copy'])
      def _shallow_copy(self, values=None, **kwargs):
          if values is not None:
              names = kwargs.pop('names', kwargs.pop('name', self.names))
              # discards freq
              kwargs.pop('freq', None)
              return MultiIndex.from_tuples(values, names=names, **kwargs)
          return self.view()
  
      @cache_readonly
      def dtype(self):
          return np.dtype('O')
  
      def _is_memory_usage_qualified(self):
          """ return a boolean if we need a qualified .info display """
          def f(l):
              return 'mixed' in l or 'string' in l or 'unicode' in l
          return any(f(l) for l in self._inferred_type_levels)
  
      @Appender(Index.memory_usage.__doc__)
      def memory_usage(self, deep=False):
          # we are overwriting our base class to avoid
          # computing .values here which could materialize
          # a tuple representation uncessarily
          return self._nbytes(deep)
  
      @cache_readonly
      def nbytes(self):
          """ return the number of bytes in the underlying data """
          return self._nbytes(False)
  
      def _nbytes(self, deep=False):
          """
          return the number of bytes in the underlying data
          deeply introspect the level data if deep=True
  
          include the engine hashtable
  
          *this is in internal routine*
  
          """
  
          # for implementations with no useful getsizeof (PyPy)
          objsize = 24
  
          level_nbytes = sum(i.memory_usage(deep=deep) for i in self.levels)
          label_nbytes = sum(i.nbytes for i in self.labels)
          names_nbytes = sum(getsizeof(i, objsize) for i in self.names)
          result = level_nbytes + label_nbytes + names_nbytes
  
          # include our engine hashtable
          result += self._engine.sizeof(deep=deep)
          return result
  
      # --------------------------------------------------------------------
      # Rendering Methods
  
      def _format_attrs(self):
          """
          Return a list of tuples of the (attr,formatted_value)
          """
          attrs = [
              ('levels', ibase.default_pprint(self._levels,
                                              max_seq_items=False)),
              ('labels', ibase.default_pprint(self._labels,
                                              max_seq_items=False))]
          if com._any_not_none(*self.names):
              attrs.append(('names', ibase.default_pprint(self.names)))
          if self.sortorder is not None:
              attrs.append(('sortorder', ibase.default_pprint(self.sortorder)))
          return attrs
  
      def _format_space(self):
          return "\n%s" % (' ' * (len(self.__class__.__name__) + 1))
  
      def _format_data(self, name=None):
          # we are formatting thru the attributes
          return None
  
      def _format_native_types(self, na_rep='nan', **kwargs):
          new_levels = []
          new_labels = []
  
          # go through the levels and format them
          for level, label in zip(self.levels, self.labels):
              level = level._format_native_types(na_rep=na_rep, **kwargs)
              # add nan values, if there are any
              mask = (label == -1)
              if mask.any():
                  nan_index = len(level)
                  level = np.append(level, na_rep)
                  label = label.values()
                  label[mask] = nan_index
              new_levels.append(level)
              new_labels.append(label)
  
          if len(new_levels) == 1:
              return Index(new_levels[0])._format_native_types()
          else:
              # reconstruct the multi-index
              mi = MultiIndex(levels=new_levels, labels=new_labels,
                              names=self.names, sortorder=self.sortorder,
                              verify_integrity=False)
              return mi.values
  
      def format(self, space=2, sparsify=None, adjoin=True, names=False,
                 na_rep=None, formatter=None):
          if len(self) == 0:
              return []
  
          stringified_levels = []
          for lev, lab in zip(self.levels, self.labels):
              na = na_rep if na_rep is not None else _get_na_rep(lev.dtype.type)
  
              if len(lev) > 0:
  
                  formatted = lev.take(lab).format(formatter=formatter)
  
                  # we have some NA
                  mask = lab == -1
                  if mask.any():
                      formatted = np.array(formatted, dtype=object)
                      formatted[mask] = na
                      formatted = formatted.tolist()
  
              else:
                  # weird all NA case
                  formatted = [pprint_thing(na if isna(x) else x,
                                            escape_chars=('\t', '\r', '\n'))
                               for x in algos.take_1d(lev._values, lab)]
              stringified_levels.append(formatted)
  
          result_levels = []
          for lev, name in zip(stringified_levels, self.names):
              level = []
  
              if names:
                  level.append(pprint_thing(name,
                                            escape_chars=('\t', '\r', '\n'))
                               if name is not None else '')
  
              level.extend(np.array(lev, dtype=object))
              result_levels.append(level)
  
          if sparsify is None:
              sparsify = get_option("display.multi_sparse")
  
          if sparsify:
              sentinel = ''
              # GH3547
              # use value of sparsify as sentinel,  unless it's an obvious
              # "Truthey" value
              if sparsify not in [True, 1]:
                  sentinel = sparsify
              # little bit of a kludge job for #1217
              result_levels = _sparsify(result_levels, start=int(names),
                                        sentinel=sentinel)
  
          if adjoin:
              from pandas.io.formats.format import _get_adjustment
              adj = _get_adjustment()
              return adj.adjoin(space, *result_levels).split('\n')
          else:
              return result_levels
  
      # --------------------------------------------------------------------
  
      def __len__(self):
          return len(self.labels[0])
  
      def _get_names(self):
          return FrozenList(level.name for level in self.levels)
  
      def _set_names(self, names, level=None, validate=True):
          """
          Set new names on index. Each name has to be a hashable type.
  
          Parameters
          ----------
          values : str or sequence
              name(s) to set
          level : int, level name, or sequence of int/level names (default None)
              If the index is a MultiIndex (hierarchical), level(s) to set (None
              for all levels).  Otherwise level must be None
          validate : boolean, default True
              validate that the names match level lengths
  
          Raises
          ------
          TypeError if each name is not hashable.
  
          Notes
          -----
          sets names on levels. WARNING: mutates!
  
          Note that you generally want to set this *after* changing levels, so
          that it only acts on copies
          """
          # GH 15110
          # Don't allow a single string for names in a MultiIndex
          if names is not None and not is_list_like(names):
              raise ValueError('Names should be list-like for a MultiIndex')
          names = list(names)
  
          if validate and level is not None and len(names) != len(level):
              raise ValueError('Length of names must match length of level.')
          if validate and level is None and len(names) != self.nlevels:
              raise ValueError('Length of names must match number of levels in '
                               'MultiIndex.')
  
          if level is None:
              level = range(self.nlevels)
          else:
              level = [self._get_level_number(l) for l in level]
  
          # set the name
          for l, name in zip(level, names):
              if name is not None:
                  # GH 20527
                  # All items in 'names' need to be hashable:
                  if not is_hashable(name):
                      raise TypeError('{}.name must be a hashable type'
                                      .format(self.__class__.__name__))
              self.levels[l].rename(name, inplace=True)
  
      names = property(fset=_set_names, fget=_get_names,
                       doc="Names of levels in MultiIndex")
  
      @Appender(_index_shared_docs['_get_grouper_for_level'])
      def _get_grouper_for_level(self, mapper, level):
          indexer = self.labels[level]
          level_index = self.levels[level]
  
          if mapper is not None:
              # Handle group mapping function and return
              level_values = self.levels[level].take(indexer)
              grouper = level_values.map(mapper)
              return grouper, None, None
  
          labels, uniques = algos.factorize(indexer, sort=True)
  
          if len(uniques) > 0 and uniques[0] == -1:
              # Handle NAs
              mask = indexer != -1
              ok_labels, uniques = algos.factorize(indexer[mask],
                                                   sort=True)
  
              labels = np.empty(len(indexer), dtype=indexer.dtype)
              labels[mask] = ok_labels
              labels[~mask] = -1
  
          if len(uniques) < len(level_index):
              # Remove unobserved levels from level_index
              level_index = level_index.take(uniques)
  
          grouper = level_index.take(labels)
  
          return grouper, labels, level_index
  
      @property
      def _constructor(self):
          return MultiIndex.from_tuples
  
      @cache_readonly
      def inferred_type(self):
          return 'mixed'
  
      def _get_level_number(self, level):
          count = self.names.count(level)
          if (count > 1) and not is_integer(level):
              raise ValueError('The name %s occurs multiple times, use a '
                               'level number' % level)
          try:
              level = self.names.index(level)
          except ValueError:
              if not is_integer(level):
                  raise KeyError('Level %s not found' % str(level))
              elif level < 0:
                  level += self.nlevels
                  if level < 0:
                      orig_level = level - self.nlevels
                      raise IndexError('Too many levels: Index has only %d '
                                       'levels, %d is not a valid level number' %
                                       (self.nlevels, orig_level))
              # Note: levels are zero-based
              elif level >= self.nlevels:
                  raise IndexError('Too many levels: Index has only %d levels, '
                                   'not %d' % (self.nlevels, level + 1))
          return level
  
      _tuples = None
  
      @cache_readonly
      def _engine(self):
          # Calculate the number of bits needed to represent labels in each
          # level, as log2 of their sizes (including -1 for NaN):
          sizes = np.ceil(np.log2([len(l) + 1 for l in self.levels]))
  
          # Sum bit counts, starting from the _right_....
          lev_bits = np.cumsum(sizes[::-1])[::-1]
  
          # ... in order to obtain offsets such that sorting the combination of
          # shifted codes (one for each level, resulting in a unique integer) is
          # equivalent to sorting lexicographically the codes themselves. Notice
          # that each level needs to be shifted by the number of bits needed to
          # represent the _previous_ ones:
          offsets = np.concatenate([lev_bits[1:], [0]]).astype('uint64')
  
          # Check the total number of bits needed for our representation:
          if lev_bits[0] > 64:
              # The levels would overflow a 64 bit uint - use Python integers:
              return MultiIndexPyIntEngine(self.levels, self.labels, offsets)
          return MultiIndexUIntEngine(self.levels, self.labels, offsets)
  
      @property
      def values(self):
          if self._tuples is not None:
              return self._tuples
  
          values = []
  
          for i in range(self.nlevels):
              vals = self._get_level_values(i)
              if is_categorical_dtype(vals):
                  vals = vals.get_values()
              if (isinstance(vals.dtype, (PandasExtensionDtype, ExtensionDtype))
                      or hasattr(vals, '_box_values')):
                  vals = vals.astype(object)
              vals = np.array(vals, copy=False)
              values.append(vals)
  
          self._tuples = lib.fast_zip(values)
          return self._tuples
  
      @property
      def _has_complex_internals(self):
          # to disable groupby tricks
          return True
  
      @cache_readonly
      def is_monotonic_increasing(self):
          """
          return if the index is monotonic increasing (only equal or
          increasing) values.
          """
  
          # reversed() because lexsort() wants the most significant key last.
          values = [self._get_level_values(i).values
                    for i in reversed(range(len(self.levels)))]
          try:
              sort_order = np.lexsort(values)
              return Index(sort_order).is_monotonic
          except TypeError:
  
              # we have mixed types and np.lexsort is not happy
              return Index(self.values).is_monotonic
  
      @cache_readonly
      def is_monotonic_decreasing(self):
          """
          return if the index is monotonic decreasing (only equal or
          decreasing) values.
          """
          # monotonic decreasing if and only if reverse is monotonic increasing
          return self[::-1].is_monotonic_increasing
  
      @cache_readonly
      def _have_mixed_levels(self):
          """ return a boolean list indicated if we have mixed levels """
          return ['mixed' in l for l in self._inferred_type_levels]
  
      @cache_readonly
      def _inferred_type_levels(self):
          """ return a list of the inferred types, one for each level """
          return [i.inferred_type for i in self.levels]
  
      @cache_readonly
      def _hashed_values(self):
          """ return a uint64 ndarray of my hashed values """
          from pandas.core.util.hashing import hash_tuples
          return hash_tuples(self)
  
      def _hashed_indexing_key(self, key):
          """
          validate and return the hash for the provided key
  
          *this is internal for use for the cython routines*
  
          Parameters
          ----------
          key : string or tuple
  
          Returns
          -------
          np.uint64
  
          Notes
          -----
          we need to stringify if we have mixed levels
  
          """
          from pandas.core.util.hashing import hash_tuples, hash_tuple
  
          if not isinstance(key, tuple):
              return hash_tuples(key)
  
          if not len(key) == self.nlevels:
              raise KeyError
  
          def f(k, stringify):
              if stringify and not isinstance(k, compat.string_types):
                  k = str(k)
              return k
          key = tuple(f(k, stringify)
                      for k, stringify in zip(key, self._have_mixed_levels))
          return hash_tuple(key)
  
      @Appender(Index.duplicated.__doc__)
      def duplicated(self, keep='first'):
          from pandas.core.sorting import get_group_index
          from pandas._libs.hashtable import duplicated_int64
  
          shape = map(len, self.levels)
          ids = get_group_index(self.labels, shape, sort=False, xnull=False)
  
          return duplicated_int64(ids, keep)
  
      def fillna(self, value=None, downcast=None):
          """
          fillna is not implemented for MultiIndex
          """
          raise NotImplementedError('isna is not defined for MultiIndex')
  
      @Appender(_index_shared_docs['dropna'])
      def dropna(self, how='any'):
          nans = [label == -1 for label in self.labels]
          if how == 'any':
              indexer = np.any(nans, axis=0)
          elif how == 'all':
              indexer = np.all(nans, axis=0)
          else:
              raise ValueError("invalid how option: {0}".format(how))
  
          new_labels = [label[~indexer] for label in self.labels]
          return self.copy(labels=new_labels, deep=True)
  
      def get_value(self, series, key):
          # somewhat broken encapsulation
          from pandas.core.indexing import maybe_droplevels
  
          # Label-based
          s = com.values_from_object(series)
          k = com.values_from_object(key)
  
          def _try_mi(k):
              # TODO: what if a level contains tuples??
              loc = self.get_loc(k)
              new_values = series._values[loc]
              new_index = self[loc]
              new_index = maybe_droplevels(new_index, k)
              return series._constructor(new_values, index=new_index,
                                         name=series.name).__finalize__(self)
  
          try:
              return self._engine.get_value(s, k)
          except KeyError as e1:
              try:
                  return _try_mi(key)
              except KeyError:
                  pass
  
              try:
                  return libindex.get_value_at(s, k)
              except IndexError:
                  raise
              except TypeError:
                  # generator/iterator-like
                  if is_iterator(key):
                      raise InvalidIndexError(key)
                  else:
                      raise e1
              except Exception:  # pragma: no cover
                  raise e1
          except TypeError:
  
              # a Timestamp will raise a TypeError in a multi-index
              # rather than a KeyError, try it here
              # note that a string that 'looks' like a Timestamp will raise
              # a KeyError! (GH5725)
              if (isinstance(key, (datetime.datetime, np.datetime64)) or
                      (compat.PY3 and isinstance(key, compat.string_types))):
                  try:
                      return _try_mi(key)
                  except KeyError:
                      raise
                  except (IndexError, ValueError, TypeError):
                      pass
  
                  try:
                      return _try_mi(Timestamp(key))
                  except (KeyError, TypeError,
                          IndexError, ValueError, tslibs.OutOfBoundsDatetime):
                      pass
  
              raise InvalidIndexError(key)
  
      def _get_level_values(self, level, unique=False):
          """
          Return vector of label values for requested level,
          equal to the length of the index
  
          **this is an internal method**
  
          Parameters
          ----------
          level : int level
          unique : bool, default False
              if True, drop duplicated values
  
          Returns
          -------
          values : ndarray
          """
  
          values = self.levels[level]
          labels = self.labels[level]
          if unique:
              labels = algos.unique(labels)
          filled = algos.take_1d(values._values, labels,
                                 fill_value=values._na_value)
          values = values._shallow_copy(filled)
          return values
  
      def get_level_values(self, level):
          """
          Return vector of label values for requested level,
          equal to the length of the index.
  
          Parameters
          ----------
          level : int or str
              ``level`` is either the integer position of the level in the
              MultiIndex, or the name of the level.
  
          Returns
          -------
          values : Index
              ``values`` is a level of this MultiIndex converted to
              a single :class:`Index` (or subclass thereof).
  
          Examples
          ---------
  
          Create a MultiIndex:
  
          >>> mi = pd.MultiIndex.from_arrays((list('abc'), list('def')))
          >>> mi.names = ['level_1', 'level_2']
  
          Get level values by supplying level as either integer or name:
  
          >>> mi.get_level_values(0)
          Index(['a', 'b', 'c'], dtype='object', name='level_1')
          >>> mi.get_level_values('level_2')
          Index(['d', 'e', 'f'], dtype='object', name='level_2')
          """
          level = self._get_level_number(level)
          values = self._get_level_values(level)
          return values
  
      @Appender(_index_shared_docs['index_unique'] % _index_doc_kwargs)
      def unique(self, level=None):
  
          if level is None:
              return super(MultiIndex, self).unique()
          else:
              level = self._get_level_number(level)
              return self._get_level_values(level=level, unique=True)
  
      def _to_safe_for_reshape(self):
          """ convert to object if we are a categorical """
          return self.set_levels([i._to_safe_for_reshape() for i in self.levels])
  
      def to_frame(self, index=True, name=None):
          """
          Create a DataFrame with the levels of the MultiIndex as columns.
  
          Column ordering is determined by the DataFrame constructor with data as
          a dict.
  
          .. versionadded:: 0.24.0
  
          Parameters
          ----------
          index : boolean, default True
              Set the index of the returned DataFrame as the original MultiIndex.
  
          name : list / sequence of strings, optional
              The passed names should substitute index level names.
  
          Returns
          -------
          DataFrame : a DataFrame containing the original MultiIndex data.
  
          See Also
          --------
          DataFrame
          """
  
          from pandas import DataFrame
          if name is not None:
              if not is_list_like(name):
                  raise TypeError("'name' must be a list / sequence "
                                  "of column names.")
  
              if len(name) != len(self.levels):
                  raise ValueError("'name' should have same length as "
                                   "number of levels on index.")
              idx_names = name
          else:
              idx_names = self.names
  
          result = DataFrame({(name or level):
                              self._get_level_values(level)
                              for name, level in
                              zip(idx_names, range(len(self.levels)))},
                             copy=False)
          if index:
              result.index = self
          return result
  
      def to_hierarchical(self, n_repeat, n_shuffle=1):
          """
          Return a MultiIndex reshaped to conform to the
          shapes given by n_repeat and n_shuffle.
  
          Useful to replicate and rearrange a MultiIndex for combination
          with another Index with n_repeat items.
  
          .. deprecated:: 0.24.0
  
          Parameters
          ----------
          n_repeat : int
              Number of times to repeat the labels on self
          n_shuffle : int
              Controls the reordering of the labels. If the result is going
              to be an inner level in a MultiIndex, n_shuffle will need to be
              greater than one. The size of each label must divisible by
              n_shuffle.
  
          Returns
          -------
          MultiIndex
  
          Examples
          --------
          >>> idx = pd.MultiIndex.from_tuples([(1, u'one'), (1, u'two'),
                                              (2, u'one'), (2, u'two')])
          >>> idx.to_hierarchical(3)
          MultiIndex(levels=[[1, 2], [u'one', u'two']],
                     labels=[[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1],
                             [0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1]])
          """
          levels = self.levels
          labels = [np.repeat(x, n_repeat) for x in self.labels]
          # Assumes that each label is divisible by n_shuffle
          labels = [x.reshape(n_shuffle, -1).ravel(order='F') for x in labels]
          names = self.names
          warnings.warn("Method .to_hierarchical is deprecated and will "
                        "be removed in a future version",
                        FutureWarning, stacklevel=2)
          return MultiIndex(levels=levels, labels=labels, names=names)
  
      def to_flat_index(self):
          """
          Convert a MultiIndex to an Index of Tuples containing the level values.
  
          .. versionadded:: 0.24.0
  
          Returns
          -------
          pd.Index
              Index with the MultiIndex data represented in Tuples.
  
          Notes
          -----
          This method will simply return the caller if called by anything other
          than a MultiIndex.
  
          Examples
          --------
          >>> index = pd.MultiIndex.from_product(
          ...     [['foo', 'bar'], ['baz', 'qux']],
          ...     names=['a', 'b'])
          >>> index.to_flat_index()
          Index([('foo', 'baz'), ('foo', 'qux'),
                 ('bar', 'baz'), ('bar', 'qux')],
                dtype='object')
          """
          return Index(self.values, tupleize_cols=False)
  
      @property
      def is_all_dates(self):
          return False
  
      def is_lexsorted(self):
          """
          Return True if the labels are lexicographically sorted
          """
          return self.lexsort_depth == self.nlevels
  
      @cache_readonly
      def lexsort_depth(self):
          if self.sortorder is not None:
              if self.sortorder == 0:
                  return self.nlevels
              else:
                  return 0
  
          int64_labels = [ensure_int64(lab) for lab in self.labels]
          for k in range(self.nlevels, 0, -1):
              if libalgos.is_lexsorted(int64_labels[:k]):
                  return k
  
          return 0
  
      def _sort_levels_monotonic(self):
          """
          .. versionadded:: 0.20.0
  
          This is an *internal* function.
  
          Create a new MultiIndex from the current to monotonically sorted
          items IN the levels. This does not actually make the entire MultiIndex
          monotonic, JUST the levels.
  
          The resulting MultiIndex will have the same outward
          appearance, meaning the same .values and ordering. It will also
          be .equals() to the original.
  
          Returns
          -------
          MultiIndex
  
          Examples
          --------
  
          >>> i = pd.MultiIndex(levels=[['a', 'b'], ['bb', 'aa']],
                                labels=[[0, 0, 1, 1], [0, 1, 0, 1]])
          >>> i
          MultiIndex(levels=[['a', 'b'], ['bb', 'aa']],
                     labels=[[0, 0, 1, 1], [0, 1, 0, 1]])
  
          >>> i.sort_monotonic()
          MultiIndex(levels=[['a', 'b'], ['aa', 'bb']],
                     labels=[[0, 0, 1, 1], [1, 0, 1, 0]])
  
          """
  
          if self.is_lexsorted() and self.is_monotonic:
              return self
  
          new_levels = []
          new_labels = []
  
          for lev, lab in zip(self.levels, self.labels):
  
              if not lev.is_monotonic:
                  try:
                      # indexer to reorder the levels
                      indexer = lev.argsort()
                  except TypeError:
                      pass
                  else:
                      lev = lev.take(indexer)
  
                      # indexer to reorder the labels
                      indexer = ensure_int64(indexer)
                      ri = lib.get_reverse_indexer(indexer, len(indexer))
                      lab = algos.take_1d(ri, lab)
  
              new_levels.append(lev)
              new_labels.append(lab)
  
          return MultiIndex(new_levels, new_labels,
                            names=self.names, sortorder=self.sortorder,
                            verify_integrity=False)
  
      def remove_unused_levels(self):
          """
          Create a new MultiIndex from the current that removes
          unused levels, meaning that they are not expressed in the labels.
  
          The resulting MultiIndex will have the same outward
          appearance, meaning the same .values and ordering. It will also
          be .equals() to the original.
  
          .. versionadded:: 0.20.0
  
          Returns
          -------
          MultiIndex
  
          Examples
          --------
          >>> i = pd.MultiIndex.from_product([range(2), list('ab')])
          MultiIndex(levels=[[0, 1], ['a', 'b']],
                     labels=[[0, 0, 1, 1], [0, 1, 0, 1]])
  
          >>> i[2:]
          MultiIndex(levels=[[0, 1], ['a', 'b']],
                     labels=[[1, 1], [0, 1]])
  
          The 0 from the first level is not represented
          and can be removed
  
          >>> i[2:].remove_unused_levels()
          MultiIndex(levels=[[1], ['a', 'b']],
                     labels=[[0, 0], [0, 1]])
          """
  
          new_levels = []
          new_labels = []
  
          changed = False
          for lev, lab in zip(self.levels, self.labels):
  
              # Since few levels are typically unused, bincount() is more
              # efficient than unique() - however it only accepts positive values
              # (and drops order):
              uniques = np.where(np.bincount(lab + 1) > 0)[0] - 1
              has_na = int(len(uniques) and (uniques[0] == -1))
  
              if len(uniques) != len(lev) + has_na:
                  # We have unused levels
                  changed = True
  
                  # Recalculate uniques, now preserving order.
                  # Can easily be cythonized by exploiting the already existing
                  # "uniques" and stop parsing "lab" when all items are found:
                  uniques = algos.unique(lab)
                  if has_na:
                      na_idx = np.where(uniques == -1)[0]
                      # Just ensure that -1 is in first position:
                      uniques[[0, na_idx[0]]] = uniques[[na_idx[0], 0]]
  
                  # labels get mapped from uniques to 0:len(uniques)
                  # -1 (if present) is mapped to last position
                  label_mapping = np.zeros(len(lev) + has_na)
                  # ... and reassigned value -1:
                  label_mapping[uniques] = np.arange(len(uniques)) - has_na
  
                  lab = label_mapping[lab]
  
                  # new levels are simple
                  lev = lev.take(uniques[has_na:])
  
              new_levels.append(lev)
              new_labels.append(lab)
  
          result = self._shallow_copy()
  
          if changed:
              result._reset_identity()
              result._set_levels(new_levels, validate=False)
              result._set_labels(new_labels, validate=False)
  
          return result
  
      @property
      def nlevels(self):
          """Integer number of levels in this MultiIndex."""
          return len(self.levels)
  
      @property
      def levshape(self):
          """A tuple with the length of each level."""
          return tuple(len(x) for x in self.levels)
  
      def __reduce__(self):
          """Necessary for making this object picklable"""
          d = dict(levels=[lev for lev in self.levels],
                   labels=[label for label in self.labels],
                   sortorder=self.sortorder, names=list(self.names))
          return ibase._new_Index, (self.__class__, d), None
  
      def __setstate__(self, state):
          """Necessary for making this object picklable"""
  
          if isinstance(state, dict):
              levels = state.get('levels')
              labels = state.get('labels')
              sortorder = state.get('sortorder')
              names = state.get('names')
  
          elif isinstance(state, tuple):
  
              nd_state, own_state = state
              levels, labels, sortorder, names = own_state
  
          self._set_levels([Index(x) for x in levels], validate=False)
          self._set_labels(labels)
          self._set_names(names)
          self.sortorder = sortorder
          self._verify_integrity()
          self._reset_identity()
  
      def __getitem__(self, key):
          if is_scalar(key):
              key = com.cast_scalar_indexer(key)
  
              retval = []
              for lev, lab in zip(self.levels, self.labels):
                  if lab[key] == -1:
                      retval.append(np.nan)
                  else:
                      retval.append(lev[lab[key]])
  
              return tuple(retval)
          else:
              if com.is_bool_indexer(key):
                  key = np.asarray(key, dtype=bool)
                  sortorder = self.sortorder
              else:
                  # cannot be sure whether the result will be sorted
                  sortorder = None
  
                  if isinstance(key, Index):
                      key = np.asarray(key)
  
              new_labels = [lab[key] for lab in self.labels]
  
              return MultiIndex(levels=self.levels, labels=new_labels,
                                names=self.names, sortorder=sortorder,
                                verify_integrity=False)
  
      @Appender(_index_shared_docs['take'] % _index_doc_kwargs)
      def take(self, indices, axis=0, allow_fill=True,
               fill_value=None, **kwargs):
          nv.validate_take(tuple(), kwargs)
          indices = ensure_platform_int(indices)
          taken = self._assert_take_fillable(self.labels, indices,
                                             allow_fill=allow_fill,
                                             fill_value=fill_value,
                                             na_value=-1)
          return MultiIndex(levels=self.levels, labels=taken,
                            names=self.names, verify_integrity=False)
  
      def _assert_take_fillable(self, values, indices, allow_fill=True,
                                fill_value=None, na_value=None):
          """ Internal method to handle NA filling of take """
          # only fill if we are passing a non-None fill_value
          if allow_fill and fill_value is not None:
              if (indices < -1).any():
                  msg = ('When allow_fill=True and fill_value is not None, '
                         'all indices must be >= -1')
                  raise ValueError(msg)
              taken = [lab.take(indices) for lab in self.labels]
              mask = indices == -1
              if mask.any():
                  masked = []
                  for new_label in taken:
                      label_values = new_label.values()
                      label_values[mask] = na_value
                      masked.append(np.asarray(label_values))
                  taken = masked
          else:
              taken = [lab.take(indices) for lab in self.labels]
          return taken
  
      def append(self, other):
          """
          Append a collection of Index options together
  
          Parameters
          ----------
          other : Index or list/tuple of indices
  
          Returns
          -------
          appended : Index
          """
          if not isinstance(other, (list, tuple)):
              other = [other]
  
          if all((isinstance(o, MultiIndex) and o.nlevels >= self.nlevels)
                 for o in other):
              arrays = []
              for i in range(self.nlevels):
                  label = self._get_level_values(i)
                  appended = [o._get_level_values(i) for o in other]
                  arrays.append(label.append(appended))
              return MultiIndex.from_arrays(arrays, names=self.names)
  
          to_concat = (self.values, ) + tuple(k._values for k in other)
          new_tuples = np.concatenate(to_concat)
  
          # if all(isinstance(x, MultiIndex) for x in other):
          try:
              return MultiIndex.from_tuples(new_tuples, names=self.names)
          except (TypeError, IndexError):
              return Index(new_tuples)
  
      def argsort(self, *args, **kwargs):
          return self.values.argsort(*args, **kwargs)
  
      def repeat(self, repeats, *args, **kwargs):
          nv.validate_repeat(args, kwargs)
          return MultiIndex(levels=self.levels,
                            labels=[label.view(np.ndarray).repeat(repeats)
                                    for label in self.labels], names=self.names,
                            sortorder=self.sortorder, verify_integrity=False)
  
      def where(self, cond, other=None):
          raise NotImplementedError(".where is not supported for "
                                    "MultiIndex operations")
  
      def drop(self, labels, level=None, errors='raise'):
          """
          Make new MultiIndex with passed list of labels deleted
  
          Parameters
          ----------
          labels : array-like
              Must be a list of tuples
          level : int or level name, default None
  
          Returns
          -------
          dropped : MultiIndex
          """
          if level is not None:
              return self._drop_from_level(labels, level)
  
          try:
              if not isinstance(labels, (np.ndarray, Index)):
                  labels = com.index_labels_to_array(labels)
              indexer = self.get_indexer(labels)
              mask = indexer == -1
              if mask.any():
                  if errors != 'ignore':
                      raise ValueError('labels %s not contained in axis' %
                                       labels[mask])
          except Exception:
              pass
  
          inds = []
          for label in labels:
              try:
                  loc = self.get_loc(label)
                  # get_loc returns either an integer, a slice, or a boolean
                  # mask
                  if isinstance(loc, int):
                      inds.append(loc)
                  elif isinstance(loc, slice):
                      inds.extend(lrange(loc.start, loc.stop))
                  elif com.is_bool_indexer(loc):
                      if self.lexsort_depth == 0:
                          warnings.warn('dropping on a non-lexsorted multi-index'
                                        ' without a level parameter may impact '
                                        'performance.',
                                        PerformanceWarning,
                                        stacklevel=3)
                      loc = loc.nonzero()[0]
                      inds.extend(loc)
                  else:
                      msg = 'unsupported indexer of type {}'.format(type(loc))
                      raise AssertionError(msg)
              except KeyError:
                  if errors != 'ignore':
                      raise
  
          return self.delete(inds)
  
      def _drop_from_level(self, labels, level):
          labels = com.index_labels_to_array(labels)
          i = self._get_level_number(level)
          index = self.levels[i]
          values = index.get_indexer(labels)
  
          mask = ~algos.isin(self.labels[i], values)
  
          return self[mask]
  
      def swaplevel(self, i=-2, j=-1):
          """
          Swap level i with level j.
  
          Calling this method does not change the ordering of the values.
  
          Parameters
          ----------
          i : int, str, default -2
              First level of index to be swapped. Can pass level name as string.
              Type of parameters can be mixed.
          j : int, str, default -1
              Second level of index to be swapped. Can pass level name as string.
              Type of parameters can be mixed.
  
          Returns
          -------
          MultiIndex
              A new MultiIndex
  
          .. versionchanged:: 0.18.1
  
             The indexes ``i`` and ``j`` are now optional, and default to
             the two innermost levels of the index.
  
          See Also
          --------
          Series.swaplevel : Swap levels i and j in a MultiIndex.
          Dataframe.swaplevel : Swap levels i and j in a MultiIndex on a
              particular axis.
  
          Examples
          --------
          >>> mi = pd.MultiIndex(levels=[['a', 'b'], ['bb', 'aa']],
          ...                    labels=[[0, 0, 1, 1], [0, 1, 0, 1]])
          >>> mi
          MultiIndex(levels=[['a', 'b'], ['bb', 'aa']],
             labels=[[0, 0, 1, 1], [0, 1, 0, 1]])
          >>> mi.swaplevel(0, 1)
          MultiIndex(levels=[['bb', 'aa'], ['a', 'b']],
             labels=[[0, 1, 0, 1], [0, 0, 1, 1]])
          """
          new_levels = list(self.levels)
          new_labels = list(self.labels)
          new_names = list(self.names)
  
          i = self._get_level_number(i)
          j = self._get_level_number(j)
  
          new_levels[i], new_levels[j] = new_levels[j], new_levels[i]
          new_labels[i], new_labels[j] = new_labels[j], new_labels[i]
          new_names[i], new_names[j] = new_names[j], new_names[i]
  
          return MultiIndex(levels=new_levels, labels=new_labels,
                            names=new_names, verify_integrity=False)
  
      def reorder_levels(self, order):
          """
          Rearrange levels using input order. May not drop or duplicate levels
  
          Parameters
          ----------
          """
          order = [self._get_level_number(i) for i in order]
          if len(order) != self.nlevels:
              raise AssertionError('Length of order must be same as '
                                   'number of levels (%d), got %d' %
                                   (self.nlevels, len(order)))
          new_levels = [self.levels[i] for i in order]
          new_labels = [self.labels[i] for i in order]
          new_names = [self.names[i] for i in order]
  
          return MultiIndex(levels=new_levels, labels=new_labels,
                            names=new_names, verify_integrity=False)
  
      def __getslice__(self, i, j):
          return self.__getitem__(slice(i, j))
  
      def _get_labels_for_sorting(self):
          """
          we categorizing our labels by using the
          available catgories (all, not just observed)
          excluding any missing ones (-1); this is in preparation
          for sorting, where we need to disambiguate that -1 is not
          a valid valid
          """
          from pandas.core.arrays import Categorical
  
          def cats(label):
              return np.arange(np.array(label).max() + 1 if len(label) else 0,
                               dtype=label.dtype)
  
          return [Categorical.from_codes(label, cats(label), ordered=True)
                  for label in self.labels]
  
      def sortlevel(self, level=0, ascending=True, sort_remaining=True):
          """
          Sort MultiIndex at the requested level. The result will respect the
          original ordering of the associated factor at that level.
  
          Parameters
          ----------
          level : list-like, int or str, default 0
              If a string is given, must be a name of the level
              If list-like must be names or ints of levels.
          ascending : boolean, default True
              False to sort in descending order
              Can also be a list to specify a directed ordering
          sort_remaining : sort by the remaining levels after level
  
          Returns
          -------
          sorted_index : pd.MultiIndex
              Resulting index
          indexer : np.ndarray
              Indices of output values in original index
          """
          from pandas.core.sorting import indexer_from_factorized
  
          if isinstance(level, (compat.string_types, int)):
              level = [level]
          level = [self._get_level_number(lev) for lev in level]
          sortorder = None
  
          # we have a directed ordering via ascending
          if isinstance(ascending, list):
              if not len(level) == len(ascending):
                  raise ValueError("level must have same length as ascending")
  
              from pandas.core.sorting import lexsort_indexer
              indexer = lexsort_indexer([self.labels[lev] for lev in level],
                                        orders=ascending)
  
          # level ordering
          else:
  
              labels = list(self.labels)
              shape = list(self.levshape)
  
              # partition labels and shape
              primary = tuple(labels.pop(lev - i) for i, lev in enumerate(level))
              primshp = tuple(shape.pop(lev - i) for i, lev in enumerate(level))
  
              if sort_remaining:
                  primary += primary + tuple(labels)
                  primshp += primshp + tuple(shape)
              else:
                  sortorder = level[0]
  
              indexer = indexer_from_factorized(primary, primshp,
                                                compress=False)
  
              if not ascending:
                  indexer = indexer[::-1]
  
          indexer = ensure_platform_int(indexer)
          new_labels = [lab.take(indexer) for lab in self.labels]
  
          new_index = MultiIndex(labels=new_labels, levels=self.levels,
                                 names=self.names, sortorder=sortorder,
                                 verify_integrity=False)
  
          return new_index, indexer
  
      def _convert_listlike_indexer(self, keyarr, kind=None):
          """
          Parameters
          ----------
          keyarr : list-like
              Indexer to convert.
  
          Returns
          -------
          tuple (indexer, keyarr)
              indexer is an ndarray or None if cannot convert
              keyarr are tuple-safe keys
          """
          indexer, keyarr = super(MultiIndex, self)._convert_listlike_indexer(
              keyarr, kind=kind)
  
          # are we indexing a specific level
          if indexer is None and len(keyarr) and not isinstance(keyarr[0],
                                                                tuple):
              level = 0
              _, indexer = self.reindex(keyarr, level=level)
  
              # take all
              if indexer is None:
                  indexer = np.arange(len(self))
  
              check = self.levels[0].get_indexer(keyarr)
              mask = check == -1
              if mask.any():
                  raise KeyError('%s not in index' % keyarr[mask])
  
          return indexer, keyarr
  
      @Appender(_index_shared_docs['get_indexer'] % _index_doc_kwargs)
      def get_indexer(self, target, method=None, limit=None, tolerance=None):
          method = missing.clean_reindex_fill_method(method)
          target = ensure_index(target)
  
          # empty indexer
          if is_list_like(target) and not len(target):
              return ensure_platform_int(np.array([]))
  
          if not isinstance(target, MultiIndex):
              try:
                  target = MultiIndex.from_tuples(target)
              except (TypeError, ValueError):
  
                  # let's instead try with a straight Index
                  if method is None:
                      return Index(self.values).get_indexer(target,
                                                            method=method,
                                                            limit=limit,
                                                            tolerance=tolerance)
  
          if not self.is_unique:
              raise ValueError('Reindexing only valid with uniquely valued '
                               'Index objects')
  
          if method == 'pad' or method == 'backfill':
              if tolerance is not None:
                  raise NotImplementedError("tolerance not implemented yet "
                                            'for MultiIndex')
              indexer = self._engine.get_indexer(target, method, limit)
          elif method == 'nearest':
              raise NotImplementedError("method='nearest' not implemented yet "
                                        'for MultiIndex; see GitHub issue 9365')
          else:
              indexer = self._engine.get_indexer(target)
  
          return ensure_platform_int(indexer)
  
      @Appender(_index_shared_docs['get_indexer_non_unique'] % _index_doc_kwargs)
      def get_indexer_non_unique(self, target):
          return super(MultiIndex, self).get_indexer_non_unique(target)
  
      def reindex(self, target, method=None, level=None, limit=None,
                  tolerance=None):
          """
          Create index with target's values (move/add/delete values as necessary)
  
          Returns
          -------
          new_index : pd.MultiIndex
              Resulting index
          indexer : np.ndarray or None
              Indices of output values in original index
  
          """
          # GH6552: preserve names when reindexing to non-named target
          # (i.e. neither Index nor Series).
          preserve_names = not hasattr(target, 'names')
  
          if level is not None:
              if method is not None:
                  raise TypeError('Fill method not supported if level passed')
  
              # GH7774: preserve dtype/tz if target is empty and not an Index.
              # target may be an iterator
              target = ibase._ensure_has_len(target)
              if len(target) == 0 and not isinstance(target, Index):
                  idx = self.levels[level]
                  attrs = idx._get_attributes_dict()
                  attrs.pop('freq', None)  # don't preserve freq
                  target = type(idx)._simple_new(np.empty(0, dtype=idx.dtype),
                                                 **attrs)
              else:
                  target = ensure_index(target)
              target, indexer, _ = self._join_level(target, level, how='right',
                                                    return_indexers=True,
                                                    keep_order=False)
          else:
              target = ensure_index(target)
              if self.equals(target):
                  indexer = None
              else:
                  if self.is_unique:
                      indexer = self.get_indexer(target, method=method,
                                                 limit=limit,
                                                 tolerance=tolerance)
                  else:
                      raise ValueError("cannot handle a non-unique multi-index!")
  
          if not isinstance(target, MultiIndex):
              if indexer is None:
                  target = self
              elif (indexer >= 0).all():
                  target = self.take(indexer)
              else:
                  # hopefully?
                  target = MultiIndex.from_tuples(target)
  
          if (preserve_names and target.nlevels == self.nlevels and
                  target.names != self.names):
              target = target.copy(deep=False)
              target.names = self.names
  
          return target, indexer
  
      def get_slice_bound(self, label, side, kind):
  
          if not isinstance(label, tuple):
              label = label,
          return self._partial_tup_index(label, side=side)
  
      def slice_locs(self, start=None, end=None, step=None, kind=None):
          """
          For an ordered MultiIndex, compute the slice locations for input
          labels.
  
          The input labels can be tuples representing partial levels, e.g. for a
          MultiIndex with 3 levels, you can pass a single value (corresponding to
          the first level), or a 1-, 2-, or 3-tuple.
  
          Parameters
          ----------
          start : label or tuple, default None
              If None, defaults to the beginning
          end : label or tuple
              If None, defaults to the end
          step : int or None
              Slice step
          kind : string, optional, defaults None
  
          Returns
          -------
          (start, end) : (int, int)
  
          Notes
          -----
          This method only works if the MultiIndex is properly lexsorted. So,
          if only the first 2 levels of a 3-level MultiIndex are lexsorted,
          you can only pass two levels to ``.slice_locs``.
  
          Examples
          --------
          >>> mi = pd.MultiIndex.from_arrays([list('abbd'), list('deff')],
          ...                                names=['A', 'B'])
  
          Get the slice locations from the beginning of 'b' in the first level
          until the end of the multiindex:
  
          >>> mi.slice_locs(start='b')
          (1, 4)
  
          Like above, but stop at the end of 'b' in the first level and 'f' in
          the second level:
  
          >>> mi.slice_locs(start='b', end=('b', 'f'))
          (1, 3)
  
          See Also
          --------
          MultiIndex.get_loc : Get location for a label or a tuple of labels.
          MultiIndex.get_locs : Get location for a label/slice/list/mask or a
                                sequence of such.
          """
          # This function adds nothing to its parent implementation (the magic
          # happens in get_slice_bound method), but it adds meaningful doc.
          return super(MultiIndex, self).slice_locs(start, end, step, kind=kind)
  
      def _partial_tup_index(self, tup, side='left'):
          if len(tup) > self.lexsort_depth:
              raise UnsortedIndexError(
                  'Key length (%d) was greater than MultiIndex'
                  ' lexsort depth (%d)' %
                  (len(tup), self.lexsort_depth))
  
          n = len(tup)
          start, end = 0, len(self)
          zipped = zip(tup, self.levels, self.labels)
          for k, (lab, lev, labs) in enumerate(zipped):
              section = labs[start:end]
  
              if lab not in lev:
                  if not lev.is_type_compatible(lib.infer_dtype([lab])):
                      raise TypeError('Level type mismatch: %s' % lab)
  
                  # short circuit
                  loc = lev.searchsorted(lab, side=side)
                  if side == 'right' and loc >= 0:
                      loc -= 1
                  return start + section.searchsorted(loc, side=side)
  
              idx = lev.get_loc(lab)
              if k < n - 1:
                  end = start + section.searchsorted(idx, side='right')
                  start = start + section.searchsorted(idx, side='left')
              else:
                  return start + section.searchsorted(idx, side=side)
  
      def get_loc(self, key, method=None):
          """
          Get location for a label or a tuple of labels as an integer, slice or
          boolean mask.
  
          Parameters
          ----------
          key : label or tuple of labels (one for each level)
          method : None
  
          Returns
          -------
          loc : int, slice object or boolean mask
              If the key is past the lexsort depth, the return may be a
              boolean mask array, otherwise it is always a slice or int.
  
          Examples
          ---------
          >>> mi = pd.MultiIndex.from_arrays([list('abb'), list('def')])
  
          >>> mi.get_loc('b')
          slice(1, 3, None)
  
          >>> mi.get_loc(('b', 'e'))
          1
  
          Notes
          ------
          The key cannot be a slice, list of same-level labels, a boolean mask,
          or a sequence of such. If you want to use those, use
          :meth:`MultiIndex.get_locs` instead.
  
          See Also
          --------
          Index.get_loc : The get_loc method for (single-level) index.
          MultiIndex.slice_locs : Get slice location given start label(s) and
                                  end label(s).
          MultiIndex.get_locs : Get location for a label/slice/list/mask or a
                                sequence of such.
          """
          if method is not None:
              raise NotImplementedError('only the default get_loc method is '
                                        'currently supported for MultiIndex')
  
          def _maybe_to_slice(loc):
              """convert integer indexer to boolean mask or slice if possible"""
              if not isinstance(loc, np.ndarray) or loc.dtype != 'int64':
                  return loc
  
              loc = lib.maybe_indices_to_slice(loc, len(self))
              if isinstance(loc, slice):
                  return loc
  
              mask = np.empty(len(self), dtype='bool')
              mask.fill(False)
              mask[loc] = True
              return mask
  
          if not isinstance(key, tuple):
              loc = self._get_level_indexer(key, level=0)
              return _maybe_to_slice(loc)
  
          keylen = len(key)
          if self.nlevels < keylen:
              raise KeyError('Key length ({0}) exceeds index depth ({1})'
                             ''.format(keylen, self.nlevels))
  
          if keylen == self.nlevels and self.is_unique:
              return self._engine.get_loc(key)
  
          # -- partial selection or non-unique index
          # break the key into 2 parts based on the lexsort_depth of the index;
          # the first part returns a continuous slice of the index; the 2nd part
          # needs linear search within the slice
          i = self.lexsort_depth
          lead_key, follow_key = key[:i], key[i:]
          start, stop = (self.slice_locs(lead_key, lead_key)
                         if lead_key else (0, len(self)))
  
          if start == stop:
              raise KeyError(key)
  
          if not follow_key:
              return slice(start, stop)
  
          warnings.warn('indexing past lexsort depth may impact performance.',
                        PerformanceWarning, stacklevel=10)
  
          loc = np.arange(start, stop, dtype='int64')
  
          for i, k in enumerate(follow_key, len(lead_key)):
              mask = self.labels[i][loc] == self.levels[i].get_loc(k)
              if not mask.all():
                  loc = loc[mask]
              if not len(loc):
                  raise KeyError(key)
  
          return (_maybe_to_slice(loc) if len(loc) != stop - start else
                  slice(start, stop))
  
      def get_loc_level(self, key, level=0, drop_level=True):
          """
          Get both the location for the requested label(s) and the
          resulting sliced index.
  
          Parameters
          ----------
          key : label or sequence of labels
          level : int/level name or list thereof, optional
          drop_level : bool, default True
              if ``False``, the resulting index will not drop any level.
  
          Returns
          -------
          loc : A 2-tuple where the elements are:
                Element 0: int, slice object or boolean array
                Element 1: The resulting sliced multiindex/index. If the key
                contains all levels, this will be ``None``.
  
          Examples
          --------
          >>> mi = pd.MultiIndex.from_arrays([list('abb'), list('def')],
          ...                                names=['A', 'B'])
  
          >>> mi.get_loc_level('b')
          (slice(1, 3, None), Index(['e', 'f'], dtype='object', name='B'))
  
          >>> mi.get_loc_level('e', level='B')
          (array([False,  True, False], dtype=bool),
          Index(['b'], dtype='object', name='A'))
  
          >>> mi.get_loc_level(['b', 'e'])
          (1, None)
  
          See Also
          ---------
          MultiIndex.get_loc  : Get location for a label or a tuple of labels.
          MultiIndex.get_locs : Get location for a label/slice/list/mask or a
                                sequence of such.
          """
  
          def maybe_droplevels(indexer, levels, drop_level):
              if not drop_level:
                  return self[indexer]
              # kludgearound
              orig_index = new_index = self[indexer]
              levels = [self._get_level_number(i) for i in levels]
              for i in sorted(levels, reverse=True):
                  try:
                      new_index = new_index.droplevel(i)
                  except ValueError:
  
                      # no dropping here
                      return orig_index
              return new_index
  
          if isinstance(level, (tuple, list)):
              if len(key) != len(level):
                  raise AssertionError('Key for location must have same '
                                       'length as number of levels')
              result = None
              for lev, k in zip(level, key):
                  loc, new_index = self.get_loc_level(k, level=lev)
                  if isinstance(loc, slice):
                      mask = np.zeros(len(self), dtype=bool)
                      mask[loc] = True
                      loc = mask
  
                  result = loc if result is None else result & loc
  
              return result, maybe_droplevels(result, level, drop_level)
  
          level = self._get_level_number(level)
  
          # kludge for #1796
          if isinstance(key, list):
              key = tuple(key)
  
          if isinstance(key, tuple) and level == 0:
  
              try:
                  if key in self.levels[0]:
                      indexer = self._get_level_indexer(key, level=level)
                      new_index = maybe_droplevels(indexer, [0], drop_level)
                      return indexer, new_index
              except TypeError:
                  pass
  
              if not any(isinstance(k, slice) for k in key):
  
                  # partial selection
                  # optionally get indexer to avoid re-calculation
                  def partial_selection(key, indexer=None):
                      if indexer is None:
                          indexer = self.get_loc(key)
                      ilevels = [i for i in range(len(key))
                                 if key[i] != slice(None, None)]
                      return indexer, maybe_droplevels(indexer, ilevels,
                                                       drop_level)
  
                  if len(key) == self.nlevels and self.is_unique:
                      # Complete key in unique index -> standard get_loc
                      return (self._engine.get_loc(key), None)
                  else:
                      return partial_selection(key)
              else:
                  indexer = None
                  for i, k in enumerate(key):
                      if not isinstance(k, slice):
                          k = self._get_level_indexer(k, level=i)
                          if isinstance(k, slice):
                              # everything
                              if k.start == 0 and k.stop == len(self):
                                  k = slice(None, None)
                          else:
                              k_index = k
  
                      if isinstance(k, slice):
                          if k == slice(None, None):
                              continue
                          else:
                              raise TypeError(key)
  
                      if indexer is None:
                          indexer = k_index
                      else:  # pragma: no cover
                          indexer &= k_index
                  if indexer is None:
                      indexer = slice(None, None)
                  ilevels = [i for i in range(len(key))
                             if key[i] != slice(None, None)]
                  return indexer, maybe_droplevels(indexer, ilevels, drop_level)
          else:
              indexer = self._get_level_indexer(key, level=level)
              return indexer, maybe_droplevels(indexer, [level], drop_level)
  
      def _get_level_indexer(self, key, level=0, indexer=None):
          # return an indexer, boolean array or a slice showing where the key is
          # in the totality of values
          # if the indexer is provided, then use this
  
          level_index = self.levels[level]
          labels = self.labels[level]
  
          def convert_indexer(start, stop, step, indexer=indexer, labels=labels):
              # given the inputs and the labels/indexer, compute an indexer set
              # if we have a provided indexer, then this need not consider
              # the entire labels set
  
              r = np.arange(start, stop, step)
              if indexer is not None and len(indexer) != len(labels):
  
                  # we have an indexer which maps the locations in the labels
                  # that we have already selected (and is not an indexer for the
                  # entire set) otherwise this is wasteful so we only need to
                  # examine locations that are in this set the only magic here is
                  # that the result are the mappings to the set that we have
                  # selected
                  from pandas import Series
                  mapper = Series(indexer)
                  indexer = labels.take(ensure_platform_int(indexer))
                  result = Series(Index(indexer).isin(r).nonzero()[0])
                  m = result.map(mapper)._ndarray_values
  
              else:
                  m = np.zeros(len(labels), dtype=bool)
                  m[np.in1d(labels, r,
                            assume_unique=Index(labels).is_unique)] = True
  
              return m
  
          if isinstance(key, slice):
              # handle a slice, returnig a slice if we can
              # otherwise a boolean indexer
  
              try:
                  if key.start is not None:
                      start = level_index.get_loc(key.start)
                  else:
                      start = 0
                  if key.stop is not None:
                      stop = level_index.get_loc(key.stop)
                  else:
                      stop = len(level_index) - 1
                  step = key.step
              except KeyError:
  
                  # we have a partial slice (like looking up a partial date
                  # string)
                  start = stop = level_index.slice_indexer(key.start, key.stop,
                                                           key.step, kind='loc')
                  step = start.step
  
              if isinstance(start, slice) or isinstance(stop, slice):
                  # we have a slice for start and/or stop
                  # a partial date slicer on a DatetimeIndex generates a slice
                  # note that the stop ALREADY includes the stopped point (if
                  # it was a string sliced)
                  return convert_indexer(start.start, stop.stop, step)
  
              elif level > 0 or self.lexsort_depth == 0 or step is not None:
                  # need to have like semantics here to right
                  # searching as when we are using a slice
                  # so include the stop+1 (so we include stop)
                  return convert_indexer(start, stop + 1, step)
              else:
                  # sorted, so can return slice object -> view
                  i = labels.searchsorted(start, side='left')
                  j = labels.searchsorted(stop, side='right')
                  return slice(i, j, step)
  
          else:
  
              code = level_index.get_loc(key)
  
              if level > 0 or self.lexsort_depth == 0:
                  # Desired level is not sorted
                  locs = np.array(labels == code, dtype=bool, copy=False)
                  if not locs.any():
                      # The label is present in self.levels[level] but unused:
                      raise KeyError(key)
                  return locs
  
              i = labels.searchsorted(code, side='left')
              j = labels.searchsorted(code, side='right')
              if i == j:
                  # The label is present in self.levels[level] but unused:
                  raise KeyError(key)
              return slice(i, j)
  
      def get_locs(self, seq):
          """
          Get location for a given label/slice/list/mask or a sequence of such as
          an array of integers.
  
          Parameters
          ----------
          seq : label/slice/list/mask or a sequence of such
             You should use one of the above for each level.
             If a level should not be used, set it to ``slice(None)``.
  
          Returns
          -------
          locs : array of integers suitable for passing to iloc
  
          Examples
          ---------
          >>> mi = pd.MultiIndex.from_arrays([list('abb'), list('def')])
  
          >>> mi.get_locs('b')
          array([1, 2], dtype=int64)
  
          >>> mi.get_locs([slice(None), ['e', 'f']])
          array([1, 2], dtype=int64)
  
          >>> mi.get_locs([[True, False, True], slice('e', 'f')])
          array([2], dtype=int64)
  
          See Also
          --------
          MultiIndex.get_loc : Get location for a label or a tuple of labels.
          MultiIndex.slice_locs : Get slice location given start label(s) and
                                  end label(s).
          """
          from .numeric import Int64Index
  
          # must be lexsorted to at least as many levels
          true_slices = [i for (i, s) in enumerate(com.is_true_slices(seq)) if s]
          if true_slices and true_slices[-1] >= self.lexsort_depth:
              raise UnsortedIndexError('MultiIndex slicing requires the index '
                                       'to be lexsorted: slicing on levels {0}, '
                                       'lexsort depth {1}'
                                       .format(true_slices, self.lexsort_depth))
          # indexer
          # this is the list of all values that we want to select
          n = len(self)
          indexer = None
  
          def _convert_to_indexer(r):
              # return an indexer
              if isinstance(r, slice):
                  m = np.zeros(n, dtype=bool)
                  m[r] = True
                  r = m.nonzero()[0]
              elif com.is_bool_indexer(r):
                  if len(r) != n:
                      raise ValueError("cannot index with a boolean indexer "
                                       "that is not the same length as the "
                                       "index")
                  r = r.nonzero()[0]
              return Int64Index(r)
  
          def _update_indexer(idxr, indexer=indexer):
              if indexer is None:
                  indexer = Index(np.arange(n))
              if idxr is None:
                  return indexer
              return indexer & idxr
  
          for i, k in enumerate(seq):
  
              if com.is_bool_indexer(k):
                  # a boolean indexer, must be the same length!
                  k = np.asarray(k)
                  indexer = _update_indexer(_convert_to_indexer(k),
                                            indexer=indexer)
  
              elif is_list_like(k):
                  # a collection of labels to include from this level (these
                  # are or'd)
                  indexers = None
                  for x in k:
                      try:
                          idxrs = _convert_to_indexer(
                              self._get_level_indexer(x, level=i,
                                                      indexer=indexer))
                          indexers = (idxrs if indexers is None
                                      else indexers | idxrs)
                      except KeyError:
  
                          # ignore not founds
                          continue
  
                  if indexers is not None:
                      indexer = _update_indexer(indexers, indexer=indexer)
                  else:
                      # no matches we are done
                      return Int64Index([])._ndarray_values
  
              elif com.is_null_slice(k):
                  # empty slice
                  indexer = _update_indexer(None, indexer=indexer)
  
              elif isinstance(k, slice):
  
                  # a slice, include BOTH of the labels
                  indexer = _update_indexer(_convert_to_indexer(
                      self._get_level_indexer(k, level=i, indexer=indexer)),
                      indexer=indexer)
              else:
                  # a single label
                  indexer = _update_indexer(_convert_to_indexer(
                      self.get_loc_level(k, level=i, drop_level=False)[0]),
                      indexer=indexer)
  
          # empty indexer
          if indexer is None:
              return Int64Index([])._ndarray_values
          return indexer._ndarray_values
  
      def truncate(self, before=None, after=None):
          """
          Slice index between two labels / tuples, return new MultiIndex
  
          Parameters
          ----------
          before : label or tuple, can be partial. Default None
              None defaults to start
          after : label or tuple, can be partial. Default None
              None defaults to end
  
          Returns
          -------
          truncated : MultiIndex
          """
          if after and before and after < before:
              raise ValueError('after < before')
  
          i, j = self.levels[0].slice_locs(before, after)
          left, right = self.slice_locs(before, after)
  
          new_levels = list(self.levels)
          new_levels[0] = new_levels[0][i:j]
  
          new_labels = [lab[left:right] for lab in self.labels]
          new_labels[0] = new_labels[0] - i
  
          return MultiIndex(levels=new_levels, labels=new_labels,
                            verify_integrity=False)
  
      def equals(self, other):
          """
          Determines if two MultiIndex objects have the same labeling information
          (the levels themselves do not necessarily have to be the same)
  
          See Also
          --------
          equal_levels
          """
          if self.is_(other):
              return True
  
          if not isinstance(other, Index):
              return False
  
          if not isinstance(other, MultiIndex):
              other_vals = com.values_from_object(ensure_index(other))
              return array_equivalent(self._ndarray_values, other_vals)
  
          if self.nlevels != other.nlevels:
              return False
  
          if len(self) != len(other):
              return False
  
          for i in range(self.nlevels):
              slabels = self.labels[i]
              slabels = slabels[slabels != -1]
              svalues = algos.take_nd(np.asarray(self.levels[i]._values),
                                      slabels, allow_fill=False)
  
              olabels = other.labels[i]
              olabels = olabels[olabels != -1]
              ovalues = algos.take_nd(
                  np.asarray(other.levels[i]._values),
                  olabels, allow_fill=False)
  
              # since we use NaT both datetime64 and timedelta64
              # we can have a situation where a level is typed say
              # timedelta64 in self (IOW it has other values than NaT)
              # but types datetime64 in other (where its all NaT)
              # but these are equivalent
              if len(svalues) == 0 and len(ovalues) == 0:
                  continue
  
              if not array_equivalent(svalues, ovalues):
                  return False
  
          return True
  
      def equal_levels(self, other):
          """
          Return True if the levels of both MultiIndex objects are the same
  
          """
          if self.nlevels != other.nlevels:
              return False
  
          for i in range(self.nlevels):
              if not self.levels[i].equals(other.levels[i]):
                  return False
          return True
  
      def union(self, other):
          """
          Form the union of two MultiIndex objects, sorting if possible
  
          Parameters
          ----------
          other : MultiIndex or array / Index of tuples
  
          Returns
          -------
          Index
  
          >>> index.union(index2)
          """
          self._assert_can_do_setop(other)
          other, result_names = self._convert_can_do_setop(other)
  
          if len(other) == 0 or self.equals(other):
              return self
  
          uniq_tuples = lib.fast_unique_multiple([self._ndarray_values,
                                                  other._ndarray_values])
          return MultiIndex.from_arrays(lzip(*uniq_tuples), sortorder=0,
                                        names=result_names)
  
      def intersection(self, other):
          """
          Form the intersection of two MultiIndex objects, sorting if possible
  
          Parameters
          ----------
          other : MultiIndex or array / Index of tuples
  
          Returns
          -------
          Index
          """
          self._assert_can_do_setop(other)
          other, result_names = self._convert_can_do_setop(other)
  
          if self.equals(other):
              return self
  
          self_tuples = self._ndarray_values
          other_tuples = other._ndarray_values
          uniq_tuples = sorted(set(self_tuples) & set(other_tuples))
          if len(uniq_tuples) == 0:
              return MultiIndex(levels=self.levels,
                                labels=[[]] * self.nlevels,
                                names=result_names, verify_integrity=False)
          else:
              return MultiIndex.from_arrays(lzip(*uniq_tuples), sortorder=0,
                                            names=result_names)
  
      def difference(self, other, sort=True):
          """
          Compute sorted set difference of two MultiIndex objects
  
          Parameters
          ----------
          other : MultiIndex
          sort : bool, default True
              Sort the resulting MultiIndex if possible
  
              .. versionadded:: 0.24.0
  
          Returns
          -------
          diff : MultiIndex
          """
          self._assert_can_do_setop(other)
          other, result_names = self._convert_can_do_setop(other)
  
          if len(other) == 0:
              return self
  
          if self.equals(other):
              return MultiIndex(levels=self.levels,
                                labels=[[]] * self.nlevels,
                                names=result_names, verify_integrity=False)
  
          this = self._get_unique_index()
  
          indexer = this.get_indexer(other)
          indexer = indexer.take((indexer != -1).nonzero()[0])
  
          label_diff = np.setdiff1d(np.arange(this.size), indexer,
                                    assume_unique=True)
          difference = this.values.take(label_diff)
          if sort:
              difference = sorted(difference)
  
          if len(difference) == 0:
              return MultiIndex(levels=[[]] * self.nlevels,
                                labels=[[]] * self.nlevels,
                                names=result_names, verify_integrity=False)
          else:
              return MultiIndex.from_tuples(difference, sortorder=0,
                                            names=result_names)
  
      @Appender(_index_shared_docs['astype'])
      def astype(self, dtype, copy=True):
          dtype = pandas_dtype(dtype)
          if is_categorical_dtype(dtype):
              msg = '> 1 ndim Categorical are not supported at this time'
              raise NotImplementedError(msg)
          elif not is_object_dtype(dtype):
              msg = ('Setting {cls} dtype to anything other than object '
                     'is not supported').format(cls=self.__class__)
              raise TypeError(msg)
          elif copy is True:
              return self._shallow_copy()
          return self
  
      def _convert_can_do_setop(self, other):
          result_names = self.names
  
          if not hasattr(other, 'names'):
              if len(other) == 0:
                  other = MultiIndex(levels=[[]] * self.nlevels,
                                     labels=[[]] * self.nlevels,
                                     verify_integrity=False)
              else:
                  msg = 'other must be a MultiIndex or a list of tuples'
                  try:
                      other = MultiIndex.from_tuples(other)
                  except TypeError:
                      raise TypeError(msg)
          else:
              result_names = self.names if self.names == other.names else None
          return other, result_names
  
      def insert(self, loc, item):
          """
          Make new MultiIndex inserting new item at location
  
          Parameters
          ----------
          loc : int
          item : tuple
              Must be same length as number of levels in the MultiIndex
  
          Returns
          -------
          new_index : Index
          """
          # Pad the key with empty strings if lower levels of the key
          # aren't specified:
          if not isinstance(item, tuple):
              item = (item, ) + ('', ) * (self.nlevels - 1)
          elif len(item) != self.nlevels:
              raise ValueError('Item must have length equal to number of '
                               'levels.')
  
          new_levels = []
          new_labels = []
          for k, level, labels in zip(item, self.levels, self.labels):
              if k not in level:
                  # have to insert into level
                  # must insert at end otherwise you have to recompute all the
                  # other labels
                  lev_loc = len(level)
                  level = level.insert(lev_loc, k)
              else:
                  lev_loc = level.get_loc(k)
  
              new_levels.append(level)
              new_labels.append(np.insert(ensure_int64(labels), loc, lev_loc))
  
          return MultiIndex(levels=new_levels, labels=new_labels,
                            names=self.names, verify_integrity=False)
  
      def delete(self, loc):
          """
          Make new index with passed location deleted
  
          Returns
          -------
          new_index : MultiIndex
          """
          new_labels = [np.delete(lab, loc) for lab in self.labels]
          return MultiIndex(levels=self.levels, labels=new_labels,
                            names=self.names, verify_integrity=False)
  
      def _wrap_joined_index(self, joined, other):
          names = self.names if self.names == other.names else None
          return MultiIndex.from_tuples(joined, names=names)
  
      @Appender(Index.isin.__doc__)
      def isin(self, values, level=None):
          if level is None:
              values = MultiIndex.from_tuples(values,
                                              names=self.names).values
              return algos.isin(self.values, values)
          else:
              num = self._get_level_number(level)
              levs = self.levels[num]
              labs = self.labels[num]
  
              sought_labels = levs.isin(values).nonzero()[0]
              if levs.size == 0:
                  return np.zeros(len(labs), dtype=np.bool_)
              else:
                  return np.lib.arraysetops.in1d(labs, sought_labels)
  
  
  MultiIndex._add_numeric_methods_disabled()
  MultiIndex._add_numeric_methods_add_sub_disabled()
  MultiIndex._add_logical_methods_disabled()
  
  
  def _sparsify(label_list, start=0, sentinel=''):
      pivoted = lzip(*label_list)
      k = len(label_list)
  
      result = pivoted[:start + 1]
      prev = pivoted[start]
  
      for cur in pivoted[start + 1:]:
          sparse_cur = []
  
          for i, (p, t) in enumerate(zip(prev, cur)):
              if i == k - 1:
                  sparse_cur.append(t)
                  result.append(sparse_cur)
                  break
  
              if p == t:
                  sparse_cur.append(sentinel)
              else:
                  sparse_cur.extend(cur[i:])
                  result.append(sparse_cur)
                  break
  
          prev = cur
  
      return lzip(*result)
  
  
  def _get_na_rep(dtype):
      return {np.datetime64: 'NaT', np.timedelta64: 'NaT'}.get(dtype, 'NaN')
  